Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917968852549632 |
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| author | Montero, Antonio Potočnik, Primož |
| author_facet | Montero, Antonio Potočnik, Primož |
| contents | The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism group (as a permutation group on the vertices). In this paper we develop some results on permutation groups (primitive and imprimitive) with small minimal degree. As a consequence of such results we classify vertex-transitive graphs whose motion is $4$ or a prime number. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_10088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree Montero, Antonio Potočnik, Primož Combinatorics Primary:05C25. Secondary: 20B25, 20B10 The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism group (as a permutation group on the vertices). In this paper we develop some results on permutation groups (primitive and imprimitive) with small minimal degree. As a consequence of such results we classify vertex-transitive graphs whose motion is $4$ or a prime number. |
| title | Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree |
| topic | Combinatorics Primary:05C25. Secondary: 20B25, 20B10 |
| url | https://arxiv.org/abs/2405.10088 |